Long-range Density Fluctuations Research Articles

Dynamical Approach to the Jamming Problem.

A simple dynamical model, biased random organization (BRO), appears to produce configurations known as random close packing (RCP) as BRO's densest critical point in dimension d=3. We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in d=1-2 (where BRO dynamics lead to crystalline order). In d=3-5, BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all investigated dimensions (d=2-5), we find that BRO belongs to the Manna universality class of dynamical phase transitions by measuring critical exponents associated with the steady-state activity and the long-range density fluctuations. Additionally, BRO's distribution of near contacts (gaps) displays behavior consistent with the infinite-dimensional theoretical treatment of RCP when d≥4. The association of BRO's densest critical configurations with random close packing implies that RCP's upper-critical dimension is consistent with the Manna class d_{uc}=4.

Ultrafast 2DIR comparison of rotational energy transfer, isolated binary collision breakdown, and near critical fluctuations in Xe and SF6 solutions.

The density dependence of rotational and vibrational energy relaxation (RER and VER) of the N2O ν3 asymmetric stretch in dense gas and supercritical Xe and SF6 solutions for near critical isotherms is measured by ultrafast 2DIR and infrared pump-probe spectroscopy. 2DIR analysis provides precise measurements of RER at all gas and supercritical solvent densities. An isolated binary collision (IBC) model is sufficient to describe RER for solvent densities ≤ ∼4M where rotational equilibrium is re-established in ∼1.5-2.5 collisions. N2O RER is ∼30% more efficient in SF6 than in Xe due to additional relaxation pathways in SF6 and electronic factor differences. 2DIR analysis revealed that N2O RER exhibits a critical slowing effect in SF6 at near critical density (ρ* ∼ 0.8) where the IBC model breaks down. This is attributable to the coupling of critical long-range density fluctuations to the local N2O free rotor environment. No such RER critical slowing is observed in Xe because IBC break down occurs much further from the Xe critical point. Many body interactions effectively shield N2O from these near critical Xe density fluctuations. The N2O ν3 VER density dependence in SF6 is different than that seen for RER, indicating a different coupling to the near critical environment than RER. N2O ν3 VER is only about ∼7 times slower than RER in SF6. In contrast, almost no VER decay is observed in Xe over 200ps. This VER solvent difference is due to a vibrationally resonant energy transfer pathway in SF6 that is not possible for Xe.

Wave transport in 1D stealthy hyperuniform phononic materials made of non-resonant and resonant scatterers

Stealthy hyperuniform point patterns are characterized by a vanishing spatial Fourier transform around the origin of the reciprocal vector space. The long-range point density fluctuations are suppressed as well in materials consisting of such distribution of scatterers, opening up opportunities to control waves. Beside wave transport in such structured materials are driven by several elements, such as the acoustic properties of the host material, the scatterer characteristics, i.e., dimensions or resonant features, and the scatterer distribution patterns. The effects of these three basic elements on the wave transport properties are usually hard to discriminate. In this work, we analyze the transport properties of acoustic waves in one-dimensional phononic materials constituted of either non-resonant or resonant scatterers distributed along stealthy hyperuniform patterns in air. The pattern is controlled by the stealthiness, allowing us to continuously vary from random phononic materials to phononic crystals. The properties of the scatterers are controlled by their size and/or the resonant frequencies. The properties of the host material are controlled by the viscothermal losses. Transport properties of stealthy hyperuniform materials are found to be robust to both the scatterer dimensions and inherent viscothermal losses, while strongly affected by the scatterer resonances, which introduce sharp dips in the transmission coefficient.

Manifestations of metastable criticality in the long-range structure of model water glasses

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index; water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids.

Design of nearly perfect hyperuniform polymeric materials.

Disordered hyperuniform materials are exotic amorphous systems that simultaneously exhibit anomalous suppression of long-range density fluctuations, comparable in amplitude to that of crystals and quasi-crystalline materials, while lacking the translational order characteristic of simple liquids. We establish a framework to quantitatively predict the emergence of hyperuniformity in polymeric materials by considering the distribution of localized polymer subregions, instead of considering the whole material. We demonstrate that this highly tunable approach results in arbitrarily small long-range density fluctuations in the liquid state. Our simulations also indicate that long-ranged density fluctuation of the whole polymeric material is remarkably insensitive to molecular topology (linear chain, unknotted ring, star, and bottlebrush) and depends on temperature in an apparently near universal fashion. Our findings open the way for the creation of nearly perfect hyperuniform polymeric materials.

Minimal statistical-mechanical model for multihyperuniform patterns in avian retina

Birds are known for their extremely acute sense of vision. The very peculiar structural distribution of five different types of cones in the retina underlies this exquisite ability to sample light. It was recently found that each cone population as well as their total population display a disordered pattern in which long-wavelength density fluctuations vanish [Jiao etal., Phys. Rev. E 89, 022721 (2014)PLEEE81539-375510.1103/PhysRevE.89.022721]. This property, known as hyperuniformity, is also present in perfect crystals. In situations like the avian retina in which both the global structure and that of each component display hyperuniformity, the system is said to be multihyperuniform. In this work, we aim at devising a minimal statistical-mechanical model that can reproduce the main features of the spatial distribution of photoreceptors in avian retina, namely the presence of disorder, multihyperuniformity, and local heterocoordination. This last feature is key to avoiding local clustering of the same type of photoreceptors, an undesirable feature for the efficient sampling of light. For this purpose, we formulate a minimal statistical-mechanical model that definitively exhibits the required structural properties: an equimolar three-component mixture (one component to sample each primary color: red, green, and blue) of nonadditive hard disks to which a long-range logarithmic repulsion is added between like particles. Interestingly, a Voronoi analysis of our idealized system of photoreceptors shows that the space-filling Voronoi polygons display a rather uniform area distribution, symmetrically centered around that of a regular lattice, a structural property also found in human retina. Disordered multihyperuniformity offers an alternative to generate photoreceptor patterns with minimal long-range concentration and density fluctuations. This is the key to overcoming the difficulties in devising an efficient visual system in which crystal-like order is absent.

Hyperuniformity order metric of Barlow packings.

The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ[over ¯]. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ[over ¯] for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ[over ¯] of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.

Hidden Hyperuniformity in Soft Polymeric Materials.

We investigate the nature of long-range density fluctuations in melts of model "soft" polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

Characterizing pixel and point patterns with a hyperuniformity disorder length.

We introduce the concept of a "hyperuniformity disorder length" h that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance h from the boundary of the window. We first compute special expectations and bounds in d dimensions, and then illustrate the range of behavior of h versus window size L by analyzing several different types of simulated two-dimensional pixel patterns-where particle positions are stored as a binary digital image in which pixels have value zero if empty and one if they contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2. Next we consider vacancy patterns, where a fraction f of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d) for small f, and h=L/2 for f→1. And finally, for a hyperuniform system with no long-range density fluctuations, we consider "Einstein patterns," where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large L,h approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to gray-scale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L) versus L. We call this approach "hyperuniformity disorder length spectroscopy".

Can a periodic boundary model reproduce the longer-range density fluctuations in a real amorphous material?

Whereas the conventional definition of the static structure factor, S(Q), means that, for any sample or structural model, its value at zero Q, S(0), is identically equal to zero, the structures of ideally-disordered materials, such as single-phase liquids and amorphous solids, incorporate long-range density fluctuations that are characterised by a non-zero limiting value (S0) of S(Q≠0) as Q→0. An analysis of these density fluctuations in terms of their Fourier components leads to the definition of an ideally-disordered material as one that exhibits a continuous, isotropic distribution of Fourier wavelengths, A(Λ), that decays asymptotically to zero at Λ=∞. On the other hand, a similar analysis for a periodic boundary model reveals that the form of the intermediate-range order at higher inter-atomic distances, r, and that of the long-range density fluctuations are fundamentally different from those of a real amorphous material. The severely limited number of (especially the longer) allowed Fourier wavelengths, Λ, coupled with their strictly defined orientations within the unit cell of a periodic boundary model, means that such a model is inherently crystalline, and that no amount of orientational (polycrystalline) averaging can overcome this problem. The various methods of deriving S(Q) for both periodic-boundary and cluster models are discussed, and it is shown that, since a periodic boundary model is not ideally-disordered, a polycrystalline average does not yield a consistent value for S0, but one that is dependent on its exact method of calculation. It is therefore concluded that, to investigate the longer-range density fluctuations in amorphous materials, it is essential to employ a cluster model, rather than one generated with a periodic boundary.

Long-Range Diffusion in Xylitol–Water Mixtures

Dynamic light scattering (DLS) and small-angle neutron scattering (SANS) were employed to study mixtures of xylitol and water. The results were also related to a previous dielectric relaxation study on the same system. In the temperature range of the DLS measurements the viscosity related structural (α) relaxation is too fast to be observed on the experimental time scale, but a considerably slower exponential and hydrodynamic relaxation process is clearly observable in the polarized light scattering data. A similar ultraslow process has been observed in many other types of binary liquids and commonly assigned to long-range concentration or density fluctuations. In some studies this interpretation has been supported by observations of substantial structural inhomogeneities in static light scattering or SANS experiments. However, in this study we observe such an ultraslow process without any indication of structural inhomogeneities on length-scales above 2 nm. Hence, we suggest that our observed ultraslow process is due to long-range diffusion of single xylitol molecules or small clusters of a few xylitol molecules (and perhaps some associated water molecules) which are randomly dispersed and sufficiently small to not be structurally detected in our SANS study. In the q-range of the DLS measurements this ultraslow relaxation process is around room temperature several orders of magnitude slower than the structural α-relaxation. However, if its 1/q(2)-dependent relaxation time is extrapolated to q-values where relaxation times from dielectric spectroscopy and quasielastic neutron scattering are compatible (about 10 nm(-1)), a relaxation time similar to that of the dielectric α-relaxation is obtained. Thus, the large difference in time scale between the two relaxation processes in the q-range of a DLS study is due to the fact that the α-relaxation is cooperative in nature, rather than caused by long-range single particle diffusion, and thus q-independent at low q-values.

Composition and Long-Range Density Fluctuations in PEO/PMMA Polymer Blends: A Result of Asymmetric Component Mobility

Fluctuations of density and composition were observed in the disordered regime of a symmetric poly(ethylene oxide) (PEO) and a poly(methyl methacrylate) (PMMA) polymer blend. This blend is of parti...

A semi-empirical molecular clustering based lattice model near to and far from the critical region

A semi-empirical molecular clustering based lattice fluid model is presented to improve the classical lattice model for volumetric properties in the critical region. This model is based on the two assumptions: (1) the Helmholtz energy is individually divided into classical and long-range density fluctuation contribution; (2) all molecules form cluster near the critical region due to long-range density fluctuation. To formulate such molecular clustering, we extended the Veytsman statistics originally developed for the cluster due to hydrogen bonding. The probability function in the statistics is modified to represent the characteristics of long-range density fluctuation vanishing far from critical region. The proposed fluctuation contribution was incorporated into the Sanchez–Lacombe model and the combined model with 6 adjustable parameters has been tested against experimental VLE data for polar and non-polar components. The combined model is found to good agreements with experimental vapor pressure, saturated density and supercritical PVT data.

Liquid Structure of and Li+ Ion Solvation in Bis(trifluoromethanesulfonyl)amide Based Ionic Liquids Composed of 1-Ethyl-3-methylimidazolium and N-Methyl-N-propylpyrrolidinium Cations

Liquid structures of the bis(trifluoromethanesulfonyl)amide based ionic liquids composed of 1-ethyl-3-methylimidazolium and N-methyl-N-propylpyrrolidinium ([C(2)mIm(+)][TFSA(-)] and [C(3)mPyrro(+)][TFSA(-)], respectively) and Li(+) ion solvation structure in their lithium salt solutions were studied by means of high-energy X-ray diffraction (HEXRD) technique with the aid of MD simulations. With regard to neat ionic liquids, a small but significant difference was found at around 3.5 Å in the intermolecular radial distribution functions G(inter)(r)s for these two ionic liquids; i.e., G(inter)(r) for [C(2)mIm(+)][TFSA(-)] was positioned at a slightly shorter region relative to that for [C(3)mPyrro(+)][TFSA(-)], which suggests that the nearest neighboring cation-anion interaction in the imidazolium ionic liquid is slightly greater than that in the other. With regard to Li(+) ion solvation structure, G(inter)(r)s for [C(2)mIm(+)][TFSA(-)] dissolving Li(+) ion exhibited additional small peak of about 1.9 Å attributable to the Li(+)-O (TFSA(-)) atom-atom correlation, though the corresponding peak was unclear in [C(3)mPyrro(+)][TFSA(-)] due to overlapping with the intramolecular atom-atom correlations in [C(3)mPyrro(+)]. In addition, the long-range density fluctuation observed in the neat ionic liquids diminished with the increase of Li(+) ion concentration for both ionic liquid solutions. These observations indicate that the large scale Li(+) ion solvated clusters are formed in the TFSA based ionic liquids, and well support the formation of [Li(TFSA)(2)](+) cluster clarified by previous Raman spectroscopic studies. MD simulations qualitatively agree with the experimental facts, by which the decrease in the long-range oscillation amplitude of r(2){G(r) - 1} for the Li(+) containing ionic liquids can be ascribed to the variation in the long-range anion-anion correlations caused by the formation of the Li(+) ion solvated clusters.

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.

10.2478/s11814-009-0350-0

This paper proposes a simple empirical correction to improve the near-critical volumetric behavior of a classical equation of state (EOS) which overpredicts the critical point. The focus is on the alternative representation of long-range density fluctuation, an effect neglected in classical EOS, in terms of molecular clustering. To formulate the molecular clustering of interest, the Veytsman statistics is extended and fluctuation parameter is explicitly obtained as a solution to the quadratic equation. The proposed contribution was combined with a quasi-chemical nonrandom lattice fluid (QLF), which overpredicts the critical point. The combined model was found to require three clustering parameters besides three classical parameters and tested against vapor-liquid equilibrium data consisting of 43 nonpolar and polar components. The calculation results showed that the combined model satisfactorily represents the flattened part of the critical isotherm curve for methane as well as the top of the coexistence curve for the tested components.

Density functional theory for calculating surface tensions with a simple renormalization formalism for the critical point

Abstract The calculation of interfacial properties, such as the surface tension, from the density functional theory suffers from the overestimation of the critical temperature of all classical Helmholtz energy functionals. A Helmholtz energy functional is here proposed, where the long-range density fluctuations leading to the universal critical scaling behavior are accounted for using a renormalization group theory. The appeal of the approach is its simple implementation, where the renormalization is treated in a local density approximation (LDA). The model is almost exact at the critical point. Away from the critical point, the model reduces to the perturbed chain statistical associated fluid theory (PC-SAFT) equation of state. The conventional PC-SAFT pure component parameters are supplemented with a single substance-specific renormalization parameter, which is adjusted to reproduce the bulk phase critical temperature. The surface tension is obtained with excellent agreement to experimental data for some non-polar and moderately polar substances (alkanes, ethers, acetates and aromatic substances) up to the critical point.

Renormalization-Group Corrections to the Perturbed-Chain Statistical Associating Fluid Theory for Binary Mixtures

Classical fluid theories do not describe the long-range fluctuations that occur in the vicinity of a pure component or mixture’s critical point. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is extended with a renormalization group theory for mixtures. The theory accounts for the long-range density fluctuations and the results reduce to the results of the classical PC-SAFT equation of state away from the critical point. Two approximation methods, the isomorphic approximation and phase-space cell approximation, are used for the renormalization group corrections of mixtures. The two variants are evaluated by comparison to experimental vapor−liquid data for systems of alkanes, carbon dioxide and hydrogen sulfide. Overall, the considered implementation of the phase-space cell approximation is slightly superior to the isomorphic approximation for the mixtures investigated here. The phase-space cell approximation tends to overestimate the renormalization corrections for so...

ChemInform Abstract: Homogeneous Organic Reactions as Mechanistic Probes in Supercritical Fluids

An interesting and intriguing aspect of supercritical fluid solutions is their microscopic inhomogeneities. The most well-known of these are the long-range densities fluctuations that occur in a pure fluid at conditions close to the critical point. However, there are also short-range inhomogeneities around dissolved solutes in supercritical fluids, which are frequently referred to as local density augmentation and local composition enhancements. Many questions have arisen about the potential influences that short-range solvation and long-range density fluctuations might have on complex chemical reaction schemes. In attempts to answer these questions, researchers have sought to study the effect of supercritical fluid solvents on simple unimolecular and bimolecular reactions. In doing so, the reactions themselves have become probes of the molecular structure and the influence of solvation on reactivity in supercritical fluids (SCFs). In this paper, the authors attempt to review those studies that involve simple reactions as probes of molecular structure and its effect on reactivity in SCFs. The paper discusses (1) the potential ways for solvation in supercritical fluids to affect reactivity and (2) the reactions that probe solvation in supercritical fluids, including diffusion-controlled reactions, kinetically-controlled reactions, equilibrium reactions, SCF solvent cage effects, and other important reactions and directions.

Density Functional Theory Integrated with Renormalization Group Theory for Criticality of Nanoconfined Fluids

Nanoconfined fluids exhibit complicated behavior such as phase transitions, prewetting, wetting transitions, universal critical properties, and critical point shifts, attributed to the cooperative interactions of short- and long-range density fluctuations. In this work, a theoretical approach, an integrated density functional (DF) and renormalization group (RG) theory, is developed to investigate the critical properties of fluids confined in slit pores or bounded by single wall surfaces. The approach can take into account both the local and the long-range density fluctuations of confined fluids self-consistently. The predicted critical order parameter exponent beta is about 1/8, and the wetting exponent beta(s) is 1.056 +/- 0.011. These values are quite close to the two-dimensional Ising values, demonstrating that the new theoretical approach is reliable as a description of criticality in nanoconfined fluids. Correspondingly, the global phase transitions and surface wetting transitions are analyzed.